## Wednesday, November 28, 2012

By Meghan Eisold

Recently, concussions have been a major concern among soccer players. When I was in high-school, some girls wore protective head gear, pictured below, to prevent concussions. I decided to determine whether the headgear can significantly lower the force that the ball exerts on a soccer player while heading the ball.
Mass of Soccer ball: 0.43 kg
Mass of soccer player’s: 75 kg
Horizontal Velocity of a kicked soccer ball(v1): 70 km/h (19.44 m/s)
I assumed that the Vertical Velocity of the ball is negligible
Horizontal velocity of soccer player (v2): -5 km/h (-1.39 m/s) (negative=direction soccer player is traveling)
Vertical Velocity of Soccer Player is assumed to be 0 (player is not jumping)

First I determined the velocity of the ball and the player after the collision:

Elastic collisions
Equation 1: m1v1 + m2v2 = m1v1+m2v2
(0.43 kg)(19.44 m/s)+(75 kg)(-1.39 m/s)=(0.43 kg)v1+(75 kg)v2
Equation 2: v1+v1= v2 + v2
(19.44 m/s) +v1= (0.43 kg) + v2
v1= v2 – 19.01
Combine equations: (0.43 kg)(19.44 m/s)+(75 kg)(-1.39 m/s)=(0.43 kg)(v2 – 19.01
m/s) +(75 kg)v2
-95.89= -8.1743 +0.43v2+(75 kg)v2’            v2=-1.16 m/s
(19.44 m/s) +v1= (1.39 m/s) + (1.60 m/s)    v1=-19.21 m/s

I then used the final velocities to determine the force that the ball would exert on the player during the appropriate collision time. I estimated that the headgear would extend the collision time by 5 ms.

Collision without headgear: t=25 ms =0.0025s
FΔ t = Δ p
Fb on p(0.0025s)=(75 kg)(-1.16 m/s)-( 75 kg)(-1.39 m/s)
Fb on p=6900 N

Collision with Collision with headgear: t=30 ms =0.0030s
FΔ t = Δ p
Fb on p(0.0030s)=(75 kg)(-1.16 m/s)-( 75 kg)(-1.39 m/s)
Fb on p=5750 N

From these results I can conclude that the headgear does lower the force that is exerted on the player, but it is not a significant difference.